To embed a tweet, use the twitter tag. The twitter button in the message format options will put it for you, or you can type it yourself if you like. The twitter tag is simply the word twitter inside of standard bbcode wrapper. Inside of the twitter tag you'll have to put the full link to the tweet like so:
And the result will be this:
To embed a youtube or vimeo video, use the youtube tag. Yeah yeah, I know. Same deal, it's the word youtube inside a bbcode rapper. You have to post a complete link to the video, not just the video ID. As such:
And the result:
You may have success getting those to show up without using the tags but the tags ensure you won't have any trouble and that everyone else will be able to see them properly. If your browser has any security extensions such as privdog, it might block embedded youtube and will probably block embedded tweets, so just be aware of that.